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2008 | 28 | 3 | 487-499
Tytuł artykułu

Order unicyclic graphs according to spectral radius of unoriented laplacian matrix

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The spectral radius of a graph is defined by that of its unoriented Laplacian matrix. In this paper, we determine the unicyclic graphs respectively with the third and the fourth largest spectral radius among all unicyclic graphs of given order.
Słowa kluczowe
Wydawca
Rocznik
Tom
28
Numer
3
Strony
487-499
Opis fizyczny
Daty
wydano
2008
otrzymano
2007-12-18
poprawiono
2008-05-13
zaakceptowano
2008-05-13
Twórcy
autor
  • Key Laboratory of Intelligent Computing & Signal Processing, Ministry of Education of the People's Republic of China, Anhui University, Hefei 230039, P.R. China
autor
  • School of Mathematics and Computation Sciences, Anhui University, Hefei, Anhui 230039, P.R. China
Bibliografia
  • [1] R.B. Bapat, J.W. Grossmana and D.M. Kulkarni, Generalized matrix tree theorem for mixed graphs, Linear Multilinear Algebra 46 (1999) 299-312, doi: 10.1080/03081089908818623.
  • [2] D. Cvetković, P. Rowlinson and S.K. Simić, Signless Laplacians of finite graphs, Linear Algebra Appl. 423 (2007) 155-171, doi: 10.1016/j.laa.2007.01.009.
  • [3] Y.-Z. Fan, On spectral integral variations of mixed graph, Linear Algebra Appl. 374 (2003) 307-316, doi: 10.1016/S0024-3795(03)00575-5.
  • [4] Y.-Z. Fan, Largest eigenvalue of a unicyclic mixed graph, Appl. Math. J. Chinese Univ. (B) 19 (2004) 140-148, doi: 10.1007/s11766-004-0047-4.
  • [5] Y.-Z. Fan, On the least eigenvalue of a unicyclic mixed graph, Linear Multilinear Algebra 53 (2005) 97-113, doi: 10.1080/03081080410001681540.
  • [6] Y.-Z. Fan, H.-Y. Hong, S.-C. Gong and Y. Wang, Order unicyclic mixed graphs by spectral radius, Australasian J. Combin. 37 (2007) 305-316.
  • [7] Y.-Z. Fan, B.-S. Tam and J. Zhou, Maximizing spectral radius of unoriented Laplacian matrix over bicyclic graphs of a 798 given order, Linear and Multilinear Algebra (2007),, doi: 10.1080/03081080701306589.
  • [8] M. Fiedler, Algebraic connectivity of graphs, Czechoslovak Math. J. 23 (1973) 298-305.
  • [9] J.W. Grossman, D.M. Kulkarni and I.E. Schochetman, Algebraic Graph Theory Without Orientation, Linear Algebra Appl. 212/213 (1994) 289-307, doi: 10.1016/0024-3795(94)90407-3.
  • [10] Y.-P. Hou, J.-S. Li and Y.-L. Pan, On the Laplacian eigenvalues of signed graphs, Linear Multilinear Algebra 51 (2003) 21-30, doi: 10.1080/0308108031000053611.
  • [11] R. Merris, Laplacian matrices of graphs: a survey, Linear Algebra Appl. 197/198 (1998) 143-176, doi: 10.1016/0024-3795(94)90486-3.
  • [12] B. Mohar, Some applications of Laplacian eigenvalues of graphs, in: Graph Symmetry (G. Hahn and G. Sabidussi Eds (Kluwer Academic Publishers, Dordrecht, 1997) 225-275.
  • [13] B.-S. Tam, Y.-Z. Fan and J. Zhou, Unoriented Laplacian maximizing graphs are degree maximal, Linear Algebra Appl. (2008), doi: 10.1016/j.laa.2008.04.002.
  • [14] X.-D. Zhang and J.-S. Li, The Laplacian spectrum of a mixed graph, Linear Algebra Appl. 353 (2002) 11-20, doi: 10.1016/S0024-3795(01)00538-9.
  • [15] X.-D. Zhang and Rong Luo, The Laplacian eigenvalues of mixed graphs, Linear Algebra Appl. 362 (2003) 109-119, doi: 10.1016/S0024-3795(02)00509-8.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1422
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